EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 18, Problem 5P
Given these data
| x | 1.6 | 2 | 2.5 | 3.2 | 4 | 4.5 |
|
|
2 | 8 | 14 | 15 | 8 | 2 |
(a) Calculate f (2.8) using Newton's interpolating polynomials of order 1 through 3. Choose the sequence of the points for your estimates to attain the best possible accuracy.
(b) Utilize Eq. (18.18) to estimate the error for each prediction.
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Your Answer:
Table Error function (erf) values
erf (z)
erf (2
erf (z)
0.55
0.5033
13
0.9340
0.025
0.0282
O 60
0.6039
14
0.9523
0.05
0.0564
0.05
0 6420
15
0.9001
0.10
0.1125
0.70
0 6778
0.9703
16
0.15
0.1080
0.75
0.7112
1.7
0.9838
0 20
0.2227
080
07421
18
0.0091
025
0 2703
0.85
0.7707
1.9
0.0028
0.30
0.3290
0.90
0.7969
20
0.9953
0.35
03704
0.95
0.8200
22
0.9981
040
0.4284
O 8427
O 8802
1.0
24
0.9903
0.45
0.4755
11
2.6
0.0098
0 50
0.5205
12
0.9103
28
0 9990
A 1010 steel is to be carburized using a gas atmosphere that produces 1.0% Cat the surface of the steel. The case depth is defined as the distance below the
surface that contains at least 0.5% Č. If carburizing is done at 1000 C, determine the time required to produce a case depth of 0 234 mm. For the diffusion of
Garbon in FCC iron Q - 137.7 kJ/mol and Do = 0.23 x 10 m²/s. The gas constant is R- 8.314 J/(mol - K). Assume that the diffusion coefficient D
remains constant and the concentrations of the diffusing atoms at the surface (c.) and at…
Chapter 18 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 18 - 18.1 Estimate the common logarithm of 10 using...Ch. 18 - 18.2 Fit a second-order Newton’s interpolating...Ch. 18 - 18.3 Fit a third-order Newton’s interpolating...Ch. 18 - Repeat Probs. 18.1 through 18.3 using the Lagrange...Ch. 18 - 18.5 Given these...Ch. 18 - 18.6 Given these data
x 1 2 3 5 7 8
...Ch. 18 - Repeat Prob. 18.6 using Lagrange polynomials of...Ch. 18 - 18.8 The following data come from a table that was...Ch. 18 - 18.9 Use Newton’s interpolating polynomial to...Ch. 18 - Use Newtons interpolating polynomial to determine...
Ch. 18 - 18.11 Employ inverse interpolation using a cubic...Ch. 18 - 18.12 Employ inverse interpolation to determine...Ch. 18 - 18.13 Develop quadratic splines for the first five...Ch. 18 - 18.14 Develop cubic splines for the data in Prob....Ch. 18 - Determine the coefficients of the parabola that...Ch. 18 - Determine the coefficients of the cubic equation...Ch. 18 - 18.17 Develop, debug, and test a program in either...Ch. 18 - 18.18 Test the program you developed in Prob....Ch. 18 - 18.19 Use the program you developed in Prob. 18.17...Ch. 18 - Use the program you developed in Prob. 18.17 to...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - 18.22 A useful application of Lagrange...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - Use the software developed in Prob. 18.23 to fit...Ch. 18 - Use the portion of the given steam table for...Ch. 18 - The following is the built-in humps function that...Ch. 18 - 18.28 The following data define the sea-level...Ch. 18 - 18.29 Generate eight equally-spaced points from...Ch. 18 - 18.30 Temperatures are measured at various points...
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